How do I extrude a shape along a curve in Blender 2.8
For some reason I thought modifiers were the "next generation" geometry tab.

Luckily it turns out I had overlooked that the geometry tab still exists in Blender 2.8!
It's the green triangle icon in the menu on the right hand side of the default layout.

From there on, it's just like in Blender 2.7, as I described in the question.

Thanks for the quick comments to my questions!